Ampère's circuital law and finite conductor

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Discussion Overview

The discussion revolves around the applicability of Ampère's circuital law to determine the electric field and magnetic field produced by a finite current-carrying conductor at a specific point in space. The scope includes theoretical considerations of electromagnetism, particularly in relation to the Biot-Savart Law and the conditions under which these laws can be applied.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether Ampère's circuital law can be applied to find the electric field for a finite conductor at a finite distance, seeking to understand the magnetic field at a specific point.
  • Another participant suggests that an infinitesimal current element can be considered, and integration across the current's strength and length can yield the desired field, referencing the Biot-Savart Law as a suitable approach.
  • Some participants argue against the use of Ampère's law, stating that changing the length of the wire would yield the same answer, which they believe undermines its applicability in this context.
  • One participant emphasizes that the derivation of Ampère's law requires the condition \nabla.J=0 everywhere, while asserting that the Biot-Savart Law can be applied more generally.
  • Another participant counters that Biot-Savart is derived from Ampère's Law and argues that Ampère's Law can be used in conjunction with Maxwell's Equations to derive the Biot-Savart Law for an infinitesimal current element.
  • There is a mention of a specific version of Ampère's law that does not include the displacement current correction.

Areas of Agreement / Disagreement

Participants express disagreement regarding the applicability of Ampère's circuital law in this scenario, with some advocating for its use and others arguing against it. The discussion remains unresolved, with multiple competing views presented.

Contextual Notes

Participants highlight limitations related to the conditions under which Ampère's law can be applied, particularly concerning the divergence of current density. The discussion also touches on the relationship between Ampère's law and the Biot-Savart Law, indicating a dependency on specific assumptions and definitions.

vijender
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Can Ampère's circuital law be used to find electric field for a finite (say length l) current carrying this conductor at a finite point away from it?
If yes, then what will be Magnetic field due to a wire extending from (0,-a/2) to (0,a/2) carrying current “I” at a point (b,0) from it, if I consider a loop (circle here) of radius b/2 perpendicular to the x-axis centered at origin?
 
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Yes. You can consider a infinitesimal current element and the resulting field. Then you integrate across the strength and length of your current. This has already been derived easily by most textbooks in the form of say the Biot-Savart Law for magnetostatics.
 
No, ampere's law can't be used here. You can always change the length of the wire and get the same answer. This absolutely can't be true
The derivation of Ampere's law requires that [tex]\nabla.J=0[/tex] everywhere. On the other hand Biot-Savart can be used anytime
 
EHT said:
No, ampere's law can't be used here. You can always change the length of the wire and get the same answer. This absolutely can't be true
The derivation of Ampere's law requires that [tex]\nabla.J=0[/tex] everywhere. On the other hand Biot-Savart can be used anytime

Biot-Savart is derived from Ampere's Law. Ampere's Law does not make any conditions upon the divergence of the current. When we talk about Ampere's Law, we are talking about the Ampere's Law as it appears in Maxwell's Equations.

Thus, the OP can use Ampere's Law (along with other Maxwell Equations) to derive the Biot-Savart Law for an infinitesimal current element (moving charge with constant velocity which thus requires a non-zero divergence in the current). Then the OP can use this as the basis for his contour integral around his arbitrarily shaped current loop as he has described previously.
 
Last edited:
as in the other thread, the ampere law that I mentioned is the one without displacement current correction in it
 

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